In order to solve the given equation, we can apply a series of the same operations on both sides of the equation, until we isolate the variable x and find its value:
[tex]\begin{gathered} 6-2\ln x=7 \\ \\ 6-2\ln x-6=7-6 \\ \\ -2\ln x=1 \\ \\ \ln x=-\frac{1}{2} \\ \\ e^{\ln x}=e^{-\frac{1}{2}} \\ \\ x=e^{-\frac{1}{2}}=\frac{1}{e^{\frac{1}{2}}}=\frac{1}{\sqrt[]{e}^{}} \end{gathered}[/tex]
Now, computing this value, and rounding to the nearest hundredth, we find:
[tex]x\cong0.61[/tex]
